S2017 E1 • Tattoos on Math

After a friend of mine got a tattoo with a representation of the cosecant function, it got me thinking about how there's another sense in which this function is a tattoo on math, so to speak.

Première diffusion : 6 janvier 2017

S2017 E2 • Fractals are typically not self-similar

What fractal dimension is, and how this is the core concept defining what fractals themselves are.

Première diffusion : 27 janvier 2017

S2017 E3 • Who (else) cares about topology? Stolen necklaces and Borsuk-Ulam

The Borsuk-Ulam theorem from topology solving a counting puzzle. Truly unexpected, truly beautiful.

Première diffusion : 10 février 2017

S2017 E4 • Euler's formula with introductory group theory

How e to the pi i can be made more intuitive with some perspectives from group theory, and why exactly e^(pi i) = -1.

Première diffusion : 3 mars 2017

S2017 E5 • Essence of calculus - Ch01

I want you to feel that you could have invented calculus for yourself, and in this first video of the series, we see how unraveling the nuances of a simple geometry question can lead to integrals, derivatives, and the fundamental theorem of calculus.

Première diffusion : 28 avril 2017

S2017 E6 • Essence of calculus - Ch02 - The paradox of the derivative

Derivatives center on the idea of change in an instant, but change happens across time while an instant consists of just one moment. How does that work?

Première diffusion : 29 avril 2017

S2017 E7 • Essence of calculus - Ch03 - Derivative formulas through geometry

A few derivative formulas, such as the power rule and the derivative of sine, demonstrated with geometric intuition.

Première diffusion : 30 avril 2017

S2017 E8 • Essence of calculus - Ch04 - Visualizing the chain rule and product rule

A visual explanation of what the chain rule and product rule are, and why they are true.

Première diffusion : 1 mai 2017

S2017 E9 • Essence of calculus - Ch05 - Derivatives of exponentials

A visual explanation of what the chain rule and product rule are, and why they are true.

Première diffusion : 2 mai 2017

S2017 E10 • Essence of calculus - Ch06 - Implicit differentiation, what's going on here?

Implicit differentiation can feel weird, but what's going on makes much more sense once you view each side of the equation as a two-variable function, f(x, y).

Première diffusion : 3 mai 2017

S2017 E11 • Essence of calculus - Ch07 - Limits

Formal derivatives, the epsilon-delta definition, and why L'Hôpital's rule works.

Première diffusion : 4 mai 2017

S2017 E12 • Essence of calculus - Ch08 - Integration and the fundamental theorem of calculus

What is an integral? How do you think about it?

Première diffusion : 5 mai 2017

S2017 E13 • Essence of calculus - Ch09 - What does area have to do with slope?

Integrals are used to find the average of a continuous variable, and this can offer a perspective on why integrals and derivatives are inverses, distinct from the one shown in the last video.

Première diffusion : 6 mai 2017

S2017 E14 • Essence of calculus - Footnote - Higher order derivatives

A very quick primer on the second derivative, third derivative, etc.

Première diffusion : 7 mai 2017

S2017 E15 • Essence of calculus - Ch10 - Taylor series

Taylor polynomials are an incredibly powerful for approximations, and Taylor series can give new ways to express functions.

Première diffusion : 7 mai 2017

S2017 E16 • Pi hiding in prime regularities

A story of pi, prime numbers, and complex numbers, and how number theory braids them together.

Première diffusion : 19 mai 2017

S2017 E17 • All possible pythagorean triples, visualized

Can we describe all right triangles with whole number side lengths using a nice pattern?

Première diffusion : 26 mai 2017

S2017 E18 • Ever wonder how Bitcoin (and other cryptocurrencies) actually work?

The Bitcoin protocol and blockchains explained from the viewpoint of stumbling into inventing your own cryptocurrency.

Première diffusion : 7 juillet 2017

S2017 E19 • How secure is 256 bit security?

Supplement to the cryptocurrency video: How hard is it to find a 256-bit hash just by guessing and checking? What kind of computer would that take?

Première diffusion : 8 juillet 2017

S2017 E20 • Hilbert's Curve: Is infinite math useful?

Space filling curves, turning visual information into audio information, and the connection between infinite and finite math.

Première diffusion : 21 juillet 2017

S2017 E21 • Thinking visually about higher dimensions

How do you think about a sphere in four dimensions? What about ten dimensions?

Première diffusion : 11 août 2017

S2017 E22 • Some light quantum mechanics

Première diffusion : 13 septembre 2017

S2017 E23 • Deep learning - Ch01 - But what *is* a Neural Network?

Première diffusion : 5 octobre 2017

S2017 E24 • Deep learning - Ch02 - Gradient descent, how neural networks learn

Première diffusion : 16 octobre 2017

S2017 E25 • Deep learning - Ch03 - What is backpropagation and what is it actually doing?

What's actually happening to a neural network as it learns?

Première diffusion : 3 novembre 2017

S2017 E26 • Deep learning - Ch03 Appendix - Backpropagation calculus

This one is a bit more symbol heavy, and that's actually the point. The goal here is to represent in somewhat more formal terms the intuition for how backpropagation works in part 3 of the series, hopefully providing some connection between that video and other texts/code that you come across later.

Première diffusion : 3 novembre 2017

S2017 E27 • The hardest problem on the hardest test

A difficult geometry puzzle with an elegant solution.

Première diffusion : 8 décembre 2017

S2017 E28 • Science YouTubers attempting a graph theory puzzle

A mug with some unexpectedly interesting math.

Première diffusion : 23 décembre 2017